Answer:
5.5<x<10.5
Step-by-step explanation:
given three side lengths, they can form a triangle if and only if the sum of any two lengths is larger than the third side. Given the side lengths for the triangle in the picture,
x + 2.5 > 8
2.5 + 8 > x
8 + x > 2.5
since the last inequality is automatically true no matter whatever length x is, we will disregard it.
now use algebraic manipulation to isolate x in each inequality
x + 2.5> 8
x + 2.5 -2.5 > 8 - 2.5
5.5<x
2.5 + 8 > x
x<10.5
by combining the two inequalities we have, we know that
5.5<x<10.5
